Diaschisma: Difference between revisions
mNo edit summary |
+wikipedia box; integrate the links to diaschismic temperaments to the temperaments section |
||
| Line 5: | Line 5: | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
{{Wikipedia| Diaschisma }} | |||
'''2048/2025''', the '''diaschisma''', | '''2048/2025''', the '''diaschisma''', a [[comma]] of 19.553 [[cent]]s, is the difference between four [[3/2|just perfect fifths]] plus two [[5/4|just major thirds]] and three octaves. It may also be defined as the difference between a Pythagorean minor seventh ([[16/9]]) and a just augmented sixth ([[225/128]]), as the difference between two classic diatonic semitones ([[16/15]]) and the major whole tone ([[9/8]]), that is, (9/8)/(16/15)<sup>2</sup>, or as the difference between the 5-limit tritone [[45/32]] and its octave complement [[64/45]]. | ||
== Temperaments == | == Temperaments == | ||
Tempering it out leads to the [[diaschismic family]] of temperaments. | Tempering it out leads to the [[diaschismic family]] of temperaments. See [[Diaschismic family]] for the rank-2 temperament family where it is tempered out. See [[Diaschismic rank three family]] for the rank-3 temperament family where it is tempered out. | ||
=== Significance === | === Significance === | ||
[http://micro.soonlabel.com/petr_parizek/pp_pump_examples/pump_1.ogg parizek1] | [http://micro.soonlabel.com/petr_parizek/pp_pump_examples/pump_1.ogg parizek1] – a [[comma pump]] progression that requires the diaschisma to be tempered out (i.e. equates two notes that are separated by a diaschisma). | ||
In the progression, the bassline moves as follows: | In the progression, the bassline moves as follows: | ||
| Line 24: | Line 25: | ||
== See also == | == See also == | ||
* [[Small comma]] | * [[Small comma]] | ||
[[Category:Diaschismic]] | [[Category:Diaschismic]] | ||